By Iam Jaebi
Updated Aug 30, 2022
In geometry, a triangle is defined by three sides that meet to form three interior angles. The sum of these angles is always 180°, so knowing two angles automatically gives the third. Special cases—equilateral triangles with equal sides and angles, and isosceles triangles with two equal sides—make many calculations straightforward. Understanding key triangle formulas lets you determine side lengths, angles, and area with confidence.
The Pythagorean theorem states that for a right‑angled triangle, the square of the hypotenuse (c) equals the sum of the squares of the other two sides (a and b): a² + b² = c². If a set of side lengths satisfies this relationship, the triangle is right‑angled.
Suppose you know one leg (a = 2) and the other leg (b = 5). Plugging these values into the theorem gives:
2² + 5² = c²
Compute the left side: 4 + 25 = 29. Thus c² = 29, and the hypotenuse is c = √29 ≈ 5.4 (rounded to one decimal place). If the equality does not hold, the triangle is not right‑angled.
The area (A) of any triangle can be found with:
A = ½ × b × h
Here, b is the base—the side resting on the horizontal plane—and h is the height—the perpendicular distance from that base to the opposite vertex.
For example, if the base is 3 units and the height is 6 units, the area calculation becomes:
A = ½ × 3 × 6 = 9
Alternatively, if you’re given the area and one side, you can rearrange the formula to solve for the missing dimension.
Assume the area is 50 units² and the height is 10 units. Plugging into the formula:
50 = ½ × b × 10
Simplify: 50 = 5b. Divide both sides by 5 to find b = 10 units.
